Symmetric duality for fractional variational problems with cone constraints

2007 ◽  
Vol 23 (1-2) ◽  
pp. 281-292
Author(s):  
I. Ahmad ◽  
Mohd. Yaqub ◽  
A. Ahmed
Keyword(s):  
Variational Problems ◽  
Symmetric Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems

scholarly journals Second order symmetric duality in fractional variational problems over cone constraints

2018 ◽  
Vol 28 (1) ◽  
pp. 39-57
Author(s):  
Anurag Jayswal ◽  
Shalini Jha
Keyword(s):  
Duality Theorem ◽  
Variational Problems ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Self Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems ◽  
Second Order Symmetric Duality ◽  
Convexity Assumptions

In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature.

scholarly journals Duality for a class of second order symmetric nondifferentiable fractional variational problems

2020 ◽  
Vol 30 (2) ◽  
pp. 121-136
Author(s):  
Ashish Prasad ◽  
Anant Singh ◽  
Sony Khatri
Keyword(s):  
Variational Problems ◽  
Second Order ◽  
Static Case ◽  
Time Dependency ◽  
Duality Theorems ◽  
Support Functions ◽  
Converse Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems ◽  
Convexity Assumptions

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

scholarly journals Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Tatiana Odzijewicz ◽  
Agnieszka B. Malinowska ◽  
Delfim F. M. Torres
Keyword(s):  
Fractional Integral ◽  
Necessary Optimality Conditions ◽  
Variational Problems ◽  
Fractional Integrals ◽  
Natural Boundary ◽  
Free Boundary Value Problems ◽  
Fractional Variational Problems ◽  
Generalized Fractional Integral ◽  
Fractional Calculus Of Variations ◽  
Natural Boundary Conditions

We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.

scholarly journals Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Jianke Zhang ◽  
Gaofeng Wang ◽  
Xiaobin Zhi ◽  
Chang Zhou
Keyword(s):  
Fractional Derivative ◽  
Lagrange Function ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Lagrange Equations ◽  
Hukuhara Difference ◽  
Generalized Hukuhara Difference ◽  
Fractional Variational Problems ◽  
Fractional Calculus Of Variations ◽  
Necessary And Sufficient

We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient optimality conditions for problems of the fuzzy fractional calculus of variations with a Lagrange function. The new kernel of gH-Atangana-Baleanu fractional derivative has no singularity and no locality, which was not precisely illustrated in the previous definitions.

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